European Journal of Mathematics and Statistics

Time Series Modeling of National Hospital Insurance Fund Coverage in Kenya

Hellen Wawira Ndwiga — 2024-12-30

National Hospital Insurance Fund (NHIF) is a state-owned organization that was established in 1966 with the goal of providing Kenyans with social health insurance that is easily accessible, affordable, long-lasting, and of high quality. Only 24% of Kenyans have access to NHIF, this may affect the implementation and outcome of Universal Health Coverage (UHC). NHIF mandate can only be achieved if the whole population is under an insurance health cover. Understanding patterns, trends and forecasting of NHIF population Coverage using time series analysis would help in policy formulation and planning for proper implementation of UHC in Kenya. The main objective of the study was to model and forecast Kenya’s NHIF population coverage using Seasonal Autoregressive Integrated Moving Average model. Time series research design was used as it involved data that was measured at regular intervals over a significant number of observations. This design followed the Box-Jenkins Seasonal Autoregressive Integrated Moving Average (SARIMA) model. Simulated time series data on NHIF enrollment for the period 1998–2023 was used for this study. R and R-studio was used in the statistical analysis of the data. The model which exhibited the least Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values was picked by fitting the SARIMA model. Finally, forecasting of the data after following the three Box-Jenkins methodologies, that is, model identification, estimation of parameters and diagnostic check is done. Having an AIC value of 2265.00 and BIC value of 2279.66 SARIMA (1,1,3) (0,1,1)4 model fitted the data well. This modelpassed residual normality test and the forecasting evaluation statistics shows the errors as RMSE = -1263.392, MAPE = 5.872978 and MAE = 11197.31 The 3-year ahead forecasts showed that the enrollment had overall increasing trend. However, moving further into the future forecast the confidence intervals tend to widen. This indicated that the model’s predictions became less certain with time. The SARIMA model proved to be a suitable approach for capturing the underlying patterns in the NHIF enrollment data, providing reasonable forecasts. The findings of the study would lead to robust sensitization by both national and county government and all other stakeholders on the importance of National Hospital Insurance Fund coverage which would lead to increased enrollment from 24% to almost 100% through the Social Health Authority (SHA). This in turn would lead to attainment of the Universal Health Coverage an objective of the third Sustainable Development Goal that stipulates healthy lives and promotes well-being for all at all ages.

A Quadratic Curve Analogue of the Taniyama-Shimura Conjecture

Masahito Hayashi — 2024-11-13

For quadratic curves over finite fileds, the number of solutions, which is governed by an analogue of the Mordell-Weil group, is expressed with the Legendre symbol of a coefficient of quadratic curves. Focusing on the number of solutions, a quadratic curve analogue of the modular form in the Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian sum and also possesses some modular transformation structure.

Solving Time-Space Fractional Boussinesq Equation Using Homotopy Perturbation Method

Meenakshi Dhumal — 2024-11-09

This paper aims to implement the homotopy perturbation technique to solve the time-space fractional Boussinesq equation, a significant model in the analysis of nonlinear wave propagation. Through the application of the homotopy perturbation technique, we derive analytical expressions for the solutions of the time-space fractional Boussinesq equation and validate these solutions through comparisons with numerical methods. Obtained results demonstrate the efficiency and accuracy of the homotopy perturbation method in solving the time-space fractional Boussinesq equation.

Introduction to the Thukral-Determinantal Formula for Accelerating Convergence of Sequence

Rajinder Kumar Thukral — 2024-06-10

There are two objectives for this paper. Firstly, we shall introduce the Thukral-determinantal formula, and secondly, we shall demonstrate the similarities between the well-established algorithms, namely the Aitkin Δ²algorithm and the Durbin sequence transformation. In fact, we have found that the solution of the Thukral-determinantal formula is equivalent to the Thukral-sequence transformation formula.

Representations of Group Algebras of Non-Abelian Groups of Orders p3, for a Prime p ≥ 3

Nabila M. Bennour — 2024-03-11

In this paper, semidirect products are used to find the matrix representations of group algebras of non-abelian groups of order p³, for a prime p ≥ 3.